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Galois automorphisms and blocks covering unipotent blocks
L. Ruhstorfer, A. A. Schaeffer Fry
In this paper we prove that a recent condition of Lyons--Martínez--Navarro--Tiep, regarding the field of values of extensions of characters in principal blocks, is satisfied for al…
The Isaacs--Navarro Galois conjecture
L. Ruhstorfer, A. A. Schaeffer Fry
We prove the original Galois refinement of the McKay conjecture, proposed by Isaacs--Navarro in 2002, providing an important subcase of the celebrated McKay--Navarro conjecture wit…
Towards the inductive McKay--Navarro Condition for groups of Lie type
Lucas Ruhstorfer, A. A. Schaeffer Fry, Britta Späth +1
We gather tools for proving the inductive McKay--Navarro (or Galois--McKay) condition for groups of Lie type and odd primes. We use this to establish a bijection in the case of qua…
The Alperin-McKay conjecture for the prime 2
Lucas Ruhstorfer
In this paper we consider the inductive Alperin-McKay condition for quasi-isolated 2-blocks of exceptional groups of Lie type. Thereby, we complete the proof of the Alperin-McKay c…
Quasi-isolated blocks and the Alperin-McKay conjecture
Lucas Ruhstorfer
The Alperin-McKay conjecture is a longstanding open conjecture in the representation theory of finite groups. Späth showed that the Alperin-McKay conjecture holds if the so-called…
Derived equivalences and equivariant Jordan decomposition
Lucas Ruhstorfer
The Bonnafé-Rouquier equivalence can be seen as a modular analogue of Lusztig's Jordan decomposition for groups of Lie type. In this paper, we show that this equivalence can be lif…